Average Error: 0.2 → 0.2
Time: 13.4s
Precision: 64
\[\left({\left(a \cdot a + b \cdot b\right)}^{2} + 4 \cdot \left(b \cdot b\right)\right) - 1\]
↓
\[\left({\left(a \cdot a + b \cdot b\right)}^{2} + 4 \cdot \left(b \cdot b\right)\right) - 1\]
\left({\left(a \cdot a + b \cdot b\right)}^{2} + 4 \cdot \left(b \cdot b\right)\right) - 1
↓
\left({\left(a \cdot a + b \cdot b\right)}^{2} + 4 \cdot \left(b \cdot b\right)\right) - 1
double f(double a, double b) {
        double r348239 = a;
        double r348240 = r348239 * r348239;
        double r348241 = b;
        double r348242 = r348241 * r348241;
        double r348243 = r348240 + r348242;
        double r348244 = 2.0;
        double r348245 = pow(r348243, r348244);
        double r348246 = 4.0;
        double r348247 = r348246 * r348242;
        double r348248 = r348245 + r348247;
        double r348249 = 1.0;
        double r348250 = r348248 - r348249;
        return r348250;
}
↓
double f(double a, double b) {
        double r348251 = a;
        double r348252 = r348251 * r348251;
        double r348253 = b;
        double r348254 = r348253 * r348253;
        double r348255 = r348252 + r348254;
        double r348256 = 2.0;
        double r348257 = pow(r348255, r348256);
        double r348258 = 4.0;
        double r348259 = r348258 * r348254;
        double r348260 = r348257 + r348259;
        double r348261 = 1.0;
        double r348262 = r348260 - r348261;
        return r348262;
}

Error

Bits error versus a

Bits error versus b

Try it out

Your Program's Arguments

Results

Enter valid numbers for all inputs

Derivation

  1. Initial program 0.2

    \[\left({\left(a \cdot a + b \cdot b\right)}^{2} + 4 \cdot \left(b \cdot b\right)\right) - 1\]

  2. Final simplification0.2

    \[\leadsto \left({\left(a \cdot a + b \cdot b\right)}^{2} + 4 \cdot \left(b \cdot b\right)\right) - 1\]

Reproduce

herbie shell --seed 2020042 
(FPCore (a b)
  :name "Bouland and Aaronson, Equation (26)"
  :precision binary64
  (- (+ (pow (+ (* a a) (* b b)) 2) (* 4 (* b b))) 1))